A Calculation Method and System for Phase Distortion Correction in Ultrasonic Imaging Based on Time Delay Estimation
By using a time delay estimation method, a phase error evaluation index is calculated using relative delay and XOR operation, and combined with a weighted average phase distortion delay, the problem of high computational complexity in existing technologies is solved, and efficient phase distortion correction for real-time ultrasound imaging is achieved.
Patent Information
- Application Number
- CN202411727813.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-28
- Publication Date
- 2025-10-31
- Estimated Expiration
- 2044-11-28
AI Technical Summary
Existing phase distortion correction techniques are computationally complex and cannot meet the computational efficiency requirements of real-time ultrasound imaging, especially in non-uniformly deformed structures where effective correction is difficult to achieve.
A time delay-based estimation method is adopted, which calculates the phase error evaluation index through relative delay and XOR operation, and performs ultrasound imaging phase distortion correction by combining weighted average phase distortion delay. The array element delay time is adjusted by using single bit word length and weighted average amplitude.
It improves the accuracy and computational efficiency of phase distortion correction, making it suitable for real-time ultrasound imaging, and particularly improves imaging quality in non-homogeneous media.
Smart Images

Figure CN119534650B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of ultrasound imaging correction technology, and relates to a calculation method and system for ultrasound imaging phase distortion correction based on time delay estimation. Background Technology
[0002] In industrial imaging, especially ultrasonic imaging, phase distortion correction technology has been widely used. For non-uniformly deformed layers, phase distortion correction can be applied as long as the reference standard is clearly defined. Furthermore, for uniformly deformed layers, phase distortion correction can also be performed if prior information about the layer thickness is available. Simultaneously, corresponding phase distortion correction methods exist for non-uniformly deformed structures, especially those with random reflector distributions. However, existing phase distortion correction techniques involve significant computation, making them more suitable for offline phase correction and less capable of meeting the computational efficiency requirements of correction algorithms for real-time ultrasonic imaging.
[0003] For example, prior art document 1 (CN200810105756.7) discloses a phase distortion correction method based on lumped correlation in phased array ultrasonic testing. When the signal-to-noise ratio of the echo signals received by the array elements is low, it can effectively improve the accuracy of time delay estimation and reduce the phase distortion between signals from different channels. The lumped correlation phase correction method selects the reference signal as the direct sum of the signals received by all array elements, performs correlation analysis between each array element and the reference signal, and calculates the time delay of each array element relative to the reference signal. However, this method involves a large amount of computation and is not suitable for real-time imaging of ultrasonic phased arrays. Summary of the Invention
[0004] To address the shortcomings of existing technologies, this invention provides a method and system for calculating phase distortion correction in ultrasound imaging based on time delay estimation. This method effectively improves the accuracy of time delay estimation and reduces phase distortion between signals in different channels, thereby meeting the requirements of real-time ultrasound imaging in industry.
[0005] The present invention adopts the following technical solution.
[0006] The first aspect of this invention provides a method for calculating phase distortion correction in ultrasound imaging based on time delay estimation, comprising:
[0007] For each array element and each scanning angle in ultrasound imaging, a phase error evaluation index is calculated based on relative delay and XOR operation, and the relative delay when the evaluation index is lower than a set threshold is obtained.
[0008] Calculate the corresponding correction delay based on the obtained relative delay, and calculate the cumulative phase distortion delay based on the correction delay;
[0009] Calculate the weighting coefficients of each array element and each scan angle in phase distortion correction, and combine them with the cumulative phase distortion delay to calculate the weighted average phase distortion delay of each array element;
[0010] The weighted average phase distortion delay is used as the array element delay time estimate for ultrasound imaging phase distortion correction.
[0011] Preferably, the formula for calculating the phase error evaluation index is:
[0012]
[0013] in, As a phase error evaluation index;
[0014] M is the length of the time window;
[0015] and Radio frequency echo samples and Shift representation;
[0016] Let be the signal value of the k-th sample of the n-th array element at the i-th scanning angle;
[0017] For the (n-1)th array element under the i-th scan angle The signal value of each sample;
[0018] The relative delay of the nth array element at the i-th scan angle;
[0019] This indicates a bit-by-bit XOR operation.
[0020] Preferably, the formula for calculating the correction delay is:
[0021]
[0022] In the formula: This is the correction delay for the nth array element at the i-th scan angle;
[0023] The relative delay of the nth array element at the i-th scan angle;
[0024] T s The sampling period for the radio frequency echo signal sample; This is a relative focus delay.
[0025] Preferably, the formula for calculating the cumulative phase distortion delay is:
[0026]
[0027] in, The cumulative phase distortion delay of the nth array element at the i-th scan angle;
[0028] This is the correction delay for the j-th array element at the i-th scan angle.
[0029] Preferably, the formula for calculating the weighting coefficient is:
[0030]
[0031] in, This represents the weighting coefficient of the nth array element at the i-th scan angle.
[0032] Let be the signal value of the k-th sample of the n-th array element at the i-th scanning angle;
[0033] M is the length of the time window.
[0034] Preferably, the formula for calculating the weighted average phase distortion delay is:
[0035]
[0036] in, The weighted average phase distortion delay of the nth array element;
[0037] This represents the weighting coefficient of the nth array element at the i-th scan angle.
[0038] The cumulative phase distortion delay of the nth array element at the i-th scan angle;
[0039] K is the number of scanning angles.
[0040] Preferably, the step of using the weighted average phase distortion delay as an estimate of the array element delay time for ultrasound imaging phase distortion correction includes:
[0041] The corresponding array element delay time is set according to the weighted average phase distortion delay of each array element, the corresponding echo amplitude signal is acquired, and imaging is performed based on the acquired signal.
[0042] A second aspect of the present invention provides an ultrasound imaging phase distortion correction calculation system based on time delay estimation, comprising:
[0043] The evaluation index calculation module is used to calculate the phase error evaluation index for each array element and each scanning angle of ultrasound imaging based on the relative delay and XOR operation, and to obtain the relative delay when the evaluation index is lower than a set threshold.
[0044] The cumulative phase distortion delay calculation module is used to calculate the corresponding correction delay based on the acquired relative delay, and to calculate the cumulative phase distortion delay based on the correction delay;
[0045] The weighted average phase distortion delay calculation module is used to calculate the weight coefficient of each array element and each scanning angle in phase distortion correction, and to calculate the weighted average phase distortion delay of each array element in combination with the cumulative phase distortion delay.
[0046] The phase distortion correction module is used to perform ultrasound imaging phase distortion correction using the weighted average phase distortion delay as an estimate of the array element delay time.
[0047] A third aspect of the present invention provides a terminal, including a processor and a storage medium; the storage medium is used to store instructions; the processor is used to perform operations according to the instructions to execute the steps of the method.
[0048] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the method.
[0049] Compared with the prior art, the beneficial effects of the present invention include at least the following:
[0050] This invention uses the absolute difference between two RF samples and SAD as phase error evaluation indicators to estimate the distortion mode of echo signals reflected by line targets and / or diffuse reflectors. It only involves addition operations, resulting in relatively low computational complexity. This phase error evaluation indicator is calculated based on relative delay and XOR operation. It utilizes the sensitivity of the XOR operation to the phase difference of the signal. When the two signals are aligned, the result of the XOR operation will be minimized, indicating that the phase distortion has been effectively corrected, and the phase error can be accurately evaluated. Furthermore, the use of a single-bit word length for bit-by-bit XOR operation, with the word length truncated to 1 bit, further improves computational efficiency. By evaluating the indicator and setting thresholds, the relative delay of adjacent array channels is effectively estimated.
[0051] This invention takes into account that an array element can only have one delay time. However, for non-uniform media, the optimal delay time may be different at multiple angles. Therefore, a weighted coefficient is introduced to calculate the weighted average phase distortion delay. The weighted coefficient for each angle is taken as the average amplitude of the echo signal received at that angle. The delay time of each array element is adjusted according to the signal strength, which can improve the accuracy of ultrasonic imaging phase distortion correction and convergence performance. Attached Figure Description
[0052] Figure 1 This is a flowchart illustrating a method for calculating phase distortion correction in ultrasound imaging based on time delay estimation, provided by the present invention. Detailed Implementation
[0053] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The embodiments described in this application are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, other embodiments obtained by those skilled in the art without creative effort are all within the protection scope of this invention.
[0054] Embodiment 1 of the present invention provides a method for calculating phase distortion correction in ultrasound imaging based on time delay estimation, such as... Figure 1 As shown, it includes:
[0055] Step 1: For each array element and each scanning angle of ultrasound imaging, calculate the phase error evaluation index based on the relative delay and XOR operation, and obtain the relative delay when the evaluation index is lower than a set threshold;
[0056] More preferably, the radio frequency echo signal samples obtained from ultrasound imaging are quantized to a single bit, and the absolute difference and SAD of ultrasound imaging in the horizontal window and time window are calculated using the radio frequency echo signal samples represented by the single bit.
[0057] First, we define the SAD (Sum of Absolute Differences) function to evaluate the relative phase difference between two sampled signals.
[0058] Within a time window of length M, the SAD of the RF echo samples received by adjacent array channels is represented as the relative delay. The function is defined by the following formula:
[0059]
[0060] in It is the k-th sample of the signal of the n-th element at the i-th scan angle;
[0061] and It is a version that is approximately shifted from each other.
[0062] More preferably, in order to address phase errors caused by multipath propagation and scattering, the present invention specifically includes:
[0063] Estimation is performed in both the horizontal and time (axial) windows, and errors are reduced by minimizing the SAD in the two-dimensional window;
[0064] To improve computational efficiency, the RF signal samples are quantized to a single bit, retaining only the zero-crossing information of the signal. The SAD calculation is performed using echo samples represented by a single bit, where each absolute difference operation is reduced to a bit-by-bit EXCLUSIVE-OR operation. operate;
[0065] Using shorter word lengths can further improve the computational efficiency of SAD technology.
[0066] The phase information of a radio frequency signal can be fully represented by the zero-crossing point of the carrier wave.
[0067] Therefore, the relative phase difference between two radio frequency signals can be easily detected from the offset of their zero-crossing points.
[0068] A single bit word is long enough to represent the zero-crossing point of the sampled signal.
[0069] Therefore, the SAD technique can appropriately quantize RF samples down to a single bit, where each absolute difference operation is reduced to a bit-by-bit EXCLUSIVE-OR.
[0070] in this case, It is given by the following formula:
[0071]
[0072] in The absolute difference and SAD of ultrasound imaging in the transverse and temporal windows are used as phase error evaluation indicators to assess the quality of phase error estimation.
[0073] M is the length of the time window, representing the number of samples considered when calculating the sum of the XOR operation results;
[0074] and These are radio frequency echo samples. and Shift representation;
[0075] Let be the signal value of the k-th sample of the n-th array element at the i-th scanning angle;
[0076] For the (n-1)th array element under the i-th scan angle The signal value of each sample;
[0077] The relative delay of the nth array element at the i-th scan angle;
[0078] This indicates that a bit-by-bit absolute difference operation is being performed.
[0079] Using single-bit quantization may worsen the convergence of speckle noise phase estimation. This effect can be mitigated by increasing the averaging rounds or using other optimization methods.
[0080] Step 2: Calculate the corresponding correction delay based on the relative delay obtained in Step 1, and calculate the cumulative phase distortion delay based on the correction delay;
[0081] The correction delay is calculated as follows:
[0082] For each n and i, find the expression that minimizes by minimizing the SAD function. After the value is found, based on the The value is calculated by taking the nth element at the i-th scan angle. The correction delay at that point is given by the formula:
[0083]
[0084] In the formula: The phase distortion delay (correction delay) of the nth array element at the i-th scan angle represents the time delay required for the signal of the nth array element in order to correct the phase distortion.
[0085] This is the relative delay corresponding to the minimum SAD.
[0086] T s The sampling period (time interval between two consecutive samples) is the sampling period of the radio frequency echo signal sample. For relative focus delay;
[0087] It is calculated assuming that the speed of sound is constant in the medium and there is no phase distortion, and can be obtained using simple geometric relationships.
[0088] The cumulative phase distortion delay of the nth element at the i-th scanning angle It is the sum of the correction delays:
[0089]
[0090] in, The cumulative phase distortion delay of the nth array element at the i-th scan angle;
[0091] Let be the phase distortion delay of the j-th array element at the i-th scan angle. It represents the time delay required for the signal of the j-th element in order to correct the phase distortion.
[0092] In practice, each It only corresponds to one This value represents the total delay from the 1st element to the nth element. For example, to calculate the total delay of the 4th element at the 3rd scan angle, then... n in formula (4) It is obtained from formula (3).
[0093] Step 3: Calculate the weighting coefficients of each array element and each scan angle in phase distortion correction, and calculate the weighted average phase distortion delay of each array element in combination with the accumulated phase distortion delay;
[0094] Further preferably, to address phase errors caused by multipath and scattering, the present invention minimizes the SAD (Signal Aberration Delay) while averaging weighted estimates across multiple scan angles to reduce the impact of multipath and scattering. The weighting coefficients are defined as the average amplitude of the echo signals received from each array element and are used for weighted average phase distortion delay calculation. Specifically:
[0095] Since the echo signal is non-uniform in angle, the estimated aberration delay needs to be appropriately weighted when averaged over a two-dimensional window;
[0096] For the i-th scan angle, the weighting coefficient of the n-th array element is defined as the average amplitude of the echo signal received from that element, i.e.:
[0097]
[0098] in, This is the weighting coefficient for the nth array element at the i-th scan angle. This formula determines the weight of that angle in phase distortion correction by calculating the average amplitude of the signal received by each array element at a specific angle. A larger weighting coefficient indicates a stronger signal at that angle, and therefore, it should be given more attention during the correction process.
[0099] Let be the signal value of the k-th sample of the n-th array element at the i-th scanning angle;
[0100] M is the length of the time window, representing the number of samples considered when calculating the average amplitude;
[0101] For each array element n, the weighted aberration delay at different scan angles i is used as a basis. and weighting coefficients Calculate the weighted average phase distortion delay The formula is:
[0102]
[0103] in, The weighted average phase distortion delay of the nth array element represents the average delay after weighting according to the weight coefficient of each angle across multiple scanning angles.
[0104] The phase distortion delay of the nth array element at the i-th scan angle;
[0105] K is the number of scanning angles used for averaging.
[0106] Step 4: Use the weighted average phase distortion delay as the array element delay time estimate to perform ultrasound imaging phase distortion correction.
[0107] More preferably, the weighted average phase distortion delay estimated in step 3 is... Ultrasonic imaging phase distortion correction includes: setting the corresponding array element delay time according to the weighted average phase distortion delay of each array element, acquiring the corresponding echo amplitude signal, and imaging based on the acquired signal.
[0108] The purpose of phase distortion correction calculation is to correct the phase error caused by the difference in sound velocity in a non-uniform medium. Correcting this error requires correcting the delay time.
[0109] By considering the phase distortion delay of each array element under different scanning angles and the corresponding weighting coefficients A comprehensive delay value is calculated. This comprehensive delay value more accurately reflects the actual phase distortion of each element at different scanning angles. The signal of each element is advanced or delayed in time according to its weighted average phase distortion delay to ensure that the signals of all elements are correctly aligned when synthesizing the ultrasonic beam. Imaging quality can be improved by optimizing beamforming.
[0110] Embodiment 2 of the present invention provides an ultrasound imaging phase distortion correction calculation system based on time delay estimation, comprising:
[0111] The evaluation index calculation module is used to calculate the phase error evaluation index for each array element and each scanning angle of ultrasound imaging based on the relative delay and XOR operation, and to obtain the relative delay when the evaluation index is lower than a set threshold.
[0112] The cumulative phase distortion delay calculation module is used to calculate the corresponding correction delay based on the acquired relative delay, and to calculate the cumulative phase distortion delay based on the correction delay;
[0113] The weighted average phase distortion delay calculation module is used to calculate the weight coefficient of each array element and each scanning angle in phase distortion correction, and to calculate the weighted average phase distortion delay of each array element in combination with the cumulative phase distortion delay.
[0114] The phase distortion correction module is used to perform ultrasound imaging phase distortion correction using the weighted average phase distortion delay as an estimate of the array element delay time.
[0115] Embodiment 3 of the present invention provides a terminal, including a processor and a storage medium; the storage medium is used to store instructions;
[0116] The processor is configured to operate according to the instructions to execute the steps of the method.
[0117] Embodiment 4 of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.
[0118] Compared with the prior art, the beneficial effects of the present invention include at least the following:
[0119] This invention estimates the distortion mode of echo signals reflected by line targets and / or diffuse reflectors based on the absolute difference between two radio frequency samples and SAD. It only involves addition operations, so the computational complexity is relatively low. This invention uses a single-bit word length for SAD calculation, and the word length is truncated to 1 bit to further improve the computational efficiency. This invention effectively estimates the relative phase error of adjacent array channels by minimizing the sum of the absolute differences between two radio frequency samples.
[0120] This invention performs a weighted average of the estimated patterns at multiple scanning angles. The weighting coefficient for each angle is the average amplitude of the echo signal received at that angle, which improves the accuracy and convergence performance of the SAD technology.
[0121] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.
[0122] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.
[0123] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.
[0124] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages such as Smalltalk, C++, etc., and conventional procedural programming languages such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.
[0125] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.
Claims
1. A method for calculating phase distortion correction in ultrasound imaging based on time delay estimation, characterized in that, include: For each array element and each scanning angle in ultrasound imaging, a phase error evaluation index is calculated based on relative delay and XOR operation. The relative delay when the evaluation index is below a set threshold is obtained. The formula for calculating the phase error evaluation index is as follows: in, M is the phase error evaluation index; M is the length of the time window; and Radio frequency echo samples and Shift representation; Let be the signal value of the k-th sample of the n-th array element at the i-th scanning angle; For the (n-1)th array element under the i-th scan angle The signal value of each sample; The relative delay of the nth array element at the i-th scan angle; This indicates a bit-by-bit XOR operation; Calculate the corresponding correction delay based on the obtained relative delay, and calculate the cumulative phase distortion delay based on the correction delay; Calculate the weighting coefficients of each array element and each scan angle in phase distortion correction, and combine them with the cumulative phase distortion delay to calculate the weighted average phase distortion delay of each array element; The weighted average phase distortion delay is used as the array element delay time estimate for ultrasound imaging phase distortion correction.
2. The method for calculating phase distortion correction in ultrasound imaging based on time delay estimation according to claim 1, characterized in that: The formula for calculating the correction delay is: In the formula: This is the correction delay for the nth array element at the i-th scan angle; The relative delay of the nth array element at the i-th scan angle; T s The sampling period for the radio frequency echo signal sample; This is a relative focus delay.
3. The method for calculating phase distortion correction in ultrasound imaging based on time delay estimation according to claim 1, characterized in that: The formula for calculating the cumulative phase distortion delay is as follows: in, The cumulative phase distortion delay of the nth array element at the i-th scan angle; This is the correction delay for the j-th array element at the i-th scan angle.
4. The method for calculating phase distortion correction in ultrasound imaging based on time delay estimation according to claim 1, characterized in that: The formula for calculating the weighting coefficient is as follows: in, This represents the weighting coefficient of the nth array element at the i-th scan angle. Let be the signal value of the k-th sample of the n-th array element at the i-th scanning angle; M is the length of the time window.
5. The method for calculating phase distortion correction in ultrasound imaging based on time delay estimation according to claim 1, characterized in that: The formula for calculating the weighted average phase distortion delay is as follows: in, The weighted average phase distortion delay of the nth array element; This represents the weighting coefficient of the nth array element at the i-th scan angle. The cumulative phase distortion delay of the nth array element at the i-th scan angle; K is the number of scanning angles.
6. The method for calculating phase distortion correction in ultrasound imaging based on time delay estimation according to claim 1, characterized in that: The step of using the weighted average phase distortion delay as an estimate of the array element delay time for ultrasound imaging phase distortion correction includes: The corresponding array element delay time is set according to the weighted average phase distortion delay of each array element, the corresponding echo amplitude signal is acquired, and imaging is performed based on the acquired signal.
7. A calculation system for ultrasonic imaging phase distortion correction based on time delay estimation, utilizing the method described in any one of claims 1-6, characterized in that, The system includes: The evaluation index calculation module is used to calculate the phase error evaluation index for each array element and each scanning angle of ultrasound imaging based on the relative delay and XOR operation, and to obtain the relative delay when the evaluation index is lower than a set threshold. The cumulative phase distortion delay calculation module is used to calculate the corresponding correction delay based on the acquired relative delay, and to calculate the cumulative phase distortion delay based on the correction delay; The weighted average phase distortion delay calculation module is used to calculate the weight coefficient of each array element and each scanning angle in phase distortion correction, and to calculate the weighted average phase distortion delay of each array element in combination with the cumulative phase distortion delay. The phase distortion correction module is used to perform ultrasound imaging phase distortion correction using the weighted average phase distortion delay as an estimate of the array element delay time.
8. A terminal, comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1-6.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1-6.
Citation Information
Patent Citations
Phase distortion emendation method based on lump correlation method in phased array ultrasonic detection
CN101403729A
Plane wave transcranial sound field phase distortion compensation method
CN113607822A
Phase distortion correction method and system for ultrasonic ring array imaging
CN117503203A